Lab 4

[BertLisser]

Ex. 2
This is no preparation for using quickCheck

-- This function creates a random set using quickcheck
-- with lowerbound a, upperbound b and maximum length n.
getRandomSetQC :: Int -> Int -> Int -> IO (Set Int)
getRandomSetQC n a b = do
    l <- getRandomListQC n a b
    let r = list2set l
    return r

-- This function creates a random list using generate and show
-- from quickcheck with lowerbound a, upperbound b and length n.
getRandomListQC :: Int -> Int -> Int -> IO ([Int])
getRandomListQC n a b = sequence (replicate n (generate (choose (a, b))))

You have to define an instance of arbitrary belonging to the type Set.
Ex. 6
This is wrong code. temp is not sorted and with duplicates.

-- Transitive closure of relation, sorted and without duplicates
trClos :: Ord a => Rel a -> Rel a
trClos xs
    | xs /= temp = trClos temp
    | otherwise = xs
    where temp = (xs `union` concat [ concat [ ([a] @@ [b]) | a <- xs, a /= b] | b <- xs])

Solution

trClos :: Ord a => Rel a -> Rel a
trClos xs
    | xs /= temp = trClos temp
    | otherwise = xs
    where temp = (sort.nub) (xs `union` concat [ concat [ ([a] @@ [b]) | a <- xs, a /= b] | b <- xs])